What they share
Both are multi-syllable classical names with deep European roots and centuries of continuous use. Both offer strong short forms (Seb, Bash; Alex, Xander, Sasha) and both pair well with shorter middle names to balance the length.
Pick Sebastian if…
Pick Sebastian if you want the softer, more artistic feel. Sebastian comes from the Greek for 'venerable' and carries a literary, slightly bohemian quality. It has none of the martial edge that Alexander can carry, and Seb as a short form is warm and easy.
Pick Alexander if…
Pick Alexander if you want the more commanding name. Alexander means 'defender of the people' and has been worn by emperors, kings, and scholars for over two thousand years. It has real heft, and the range of nicknames means you can soften it or keep it formal.
Alexander is the heavier of the two; Sebastian the more romantic. Both age into adulthood with authority. If the full name feels too long for daily use, consider which short form you are most drawn to; that usually settles the question.